Tesis doctorales: TESEO

Ayuda Salir

Ficha de Tesis

Imprimir

Ministerio de Universidades - Gobierno de España

Título: DISCRETE COMPLEX REDUNDANT SYSTEMS WITH LOSS OF UNITS AND AN INDETERMINATE NUMBER OF REPAIRPERSONS
Autor: A S DAWABSHA, MOHAMMED
Universidad: Universidad de Granada
Departamento: Estadística e investigación operativa
Fecha de Lectura: 22/10/2018
Programa de doctorado: Programa de Doctorado en Estadística Matemática y Aplicada por la Universidad de Granada
Dirección:
- RUÍZ CASTRO, JUAN ELOY (DIRECTOR)
Tribunal:
- Valderrama Bonnet, Mariano (PRESIDENTE)
- AGUILERA DEL PINO, ANA MARIA (SECRETARIO)
- RUÍZ MOLINA, JUAN CARLOS (VOCAL)
- BARRANCO CHAMORRO, INMACULADA (VOCAL)
- LILLO RODRIGUEZ, ROSA E. (VOCAL)
Descriptores:
- FIABILIDAD DE SISTEMAS
- PROCESOS DE MARKOV
- PROBABILIDAD
Fichero de tesis:
ISBN: 9788413060026

http://digibug.ugr.es/bitstream/handle/10481/53795/29124736.pdf?sequence=4&isAllowed=yhttp://

Marcador: https://www.educacion.gob.es/teseo/mostrarRef.do?ref=1717068Añadir a favoritos.
Resumen:
Summary DISCRETE COMPLEX REDUNDANT SYSTEMS WITH LOSS OF UNITS AND AN INDETERMINATE NUMBER OF REPAIRPERSONS Mohammed A S Dawabsha The overall aim of this project is to model complex systems that evolve in discrete time through Markovian Arrival Processes with marked arrivals (D-MMAP) in an algorithmic and computational form. These systems are subject to several types of failure, repairable and/or non-repairable, as a consequence of internal wear or external shocks. Random inspections are included in the models and preventive maintenance is carried out as a consequence of this. Loss of units is introduced; i.e. each time that a non-repairable occurs, it is removed and no replaced. Variable numbers of repairpersons are considered; i.e. each time that a non-repairable occurs, (the number of repairpersons changes and depends on the number of units in the system). The system will be optimised by considering two different standpoints: the profitability of preventive maintenance and the number of repairpersons present according to the number of units in the system. The main objective is to develop complex multi-state systems; complex unit-system, complex cold standby systems, complex warm standby systems and k-out-of-n: G system, in a well-structured and algorithmic form. The following aspects are analyzed for each system proposed. ¿ The system is subject to multiple failure factors (internal and accidental external failures, repairable or non-repairable). ¿ Preventive maintenance is included as a consequence of random inspections. ¿ We build new models with loss of units and with a non-fixed number of repairpersons. The number of repairpersons will vary according to the number of units in the system. ¿ Phase type distributions and D-MMAPs are considered in the modelling. Thus, the results are given in an algorithmic and computational way. ¿ A transient analysis is carried out and the stationary distribution is worked out by considering matrix analytic methods. ¿ For both cases, transient and stationary regime, several reliability measures of interest such as the availability, reliability, conditional probability of different types of failures, etcetera are calculated in a well-structured way. ¿ Rewards and costs are included in the models to optimize the behavior of the system according to preventive maintenance and number of repairpersons. ¿ All results are expressed in algorithmic and computational form and they have been implemented computationally with Matlab. This work has been performed in a sequential form, from a multi-state complex one-unit system to complex redundant systems. ¿ Chapter 1 presents the basic theory that is going to play an important role throughout this work. Phase type distributions, Markovian Arrival Processes, BMAP, MMAP, Costs, etc will be introduced in this chapter. ¿ Chapter 2 analyzes the behavior of one unit multi-state dynamic system subject to multiple events through a Markovian arrival process with marked arrivals (MMAP). This study considers if preventive maintenance is profitable or not, and also shows how the system can be optimised according to its internal performance and the external cumulative damage states revealed by inspection. A numerical example, optimising the system by determining the optimum states from an economic standpoint, illustrates the versatility of the model proposed. ¿ Chapter 3 describes cold standby systems with multiple variable repairpersons, evolving in discrete time. The online unit works as the one of chapter 2. This complex system is modelled by a MMAP in an algorithmic and computational form. Two interesting contributions are made in the present study. The number of repairpersons is indeterminate and variable depending on the number of units in the system. ¿ Chapter 4 shows complex multi-state warm standby systems subject to different types of failures with loss of units. In this study we extend chapter 3 to the warms standby case. We model general reliability systems and associated measures to analyse the behaviour and effectiveness of preventive maintenance depending on the number of repairpersons and net rewards. ¿ Chapter 5 describes a multi-state complex k-out-of-n: G system with loss of units. It is modelled in an algorithmic and computational form. Several interesting reliability measures are obtained, for both transient and stationary regimes. A numerical example is given to show the versatility of the model. The main references used in this work are the following. [1] Alfa A.S. (2016) Applied discrete-time queues. Springer Science+Business Media New York. [2] Artalejo, J. R.: Gómez-Corral, A. and He, Q.M. (2010) Markovian arrivals in stochastic modelling: a survey and some new results. Statistics and Operations Research Transactions, 34, 2, 101¿144. [3] Barbu, V.S. and Limnios, N. (2008) Reliability of Semi-Markov Systems in Discrete Time: Modeling and Estimation. In: Handbook of Performability Engineering, 369¿380. Springer, London. [4] Birnbaum, Z.W.; Esary, J.D. and Saunders, S.C. (1961) Multicomponent systems and structures and their reliability. Technometrics, 3, 55¿77. [5] Bobbio A, Hovarth A, Scarpa M, Telek M (2004) Acyclic discrete phase type distributions: properties and a parameter estimation algorithm. Performance Evaluation, 54,1¿32. [6] Buchholz, P.; Kriege, J. and Felko, I. (2014) Input modeling with phase-type distributions and Markov models. Theory and Applications. Springer Cham Heidelberg New York Dordrecht London. [7] Cui, L. and Xie, M. (2005) On a generalized k-out-of-n system and its reliability. International Journal of Systems Science, 36, 5, 267¿274. [8] Dafermos, S. and Neuts, M.F. (1971): A single server queue in discrete time. Cahiers du Centre Recherche operationelle, 13, 23-40. [9] Daneshkhah, A.; Stocks, N.G. and Jeffrey, P. (2017) Probabilistic sensitivity analysis of optimised preventive maintenance strategies for deteriorating infrastructure assets. Reliability Engineering and System Safety, 163, 33¿45. [10] Das, S.; Dewanji, A. and Segupta D. (2016) Discrete time software reliability modeling with periodic debugging schedule. Statistical Methodology, 33, 147¿159. [11] Dewanji, A.; Segupta, D. and Chakraborty, K. (2011) A discrete time model for software reliability with application to a flight control software. Applied Stochastic Models in Business and Industry, 27, 6, 723¿731. [12] El-Neweihi, E. and Proschan, F. (1984) Degradable systems: a survey of multistate system theory. Commun Stat Theory Methods, 13, 405¿432. [13] Eryilmaz, S. (2010) Mean Residual and Mean Past Lifetime of Multi-State Systems With Identical Components. IEEE Transactions on Reliability, 59, 4, 644¿649. [14] Galliher, H. P. and Wheeler, R. C. (1958). Nonstationary Queuing Probabilities for Landing Congestion of Aircraft. Operations Research, 6, 2, 264¿275. [15] Georgiadis, S. and Limnios, N. (2014) Interval reliability for semi-Markov systems in discrete time. Journal de la Société Française de Statistique, 153, 3, 152¿166. [16] He, Q-M. (2014) Fundamentals of Matrix-Analytic Methods. Springer, New York. [17] Huilin Y.; Xiaohan Y. and Peng, R. (2015) Generalized Accelerated Failure Time Frailty Model for Systems Subject to Imperfect Preventive Maintenance. Mathematical Problems in Engineering, 2015, Article ID 908742, 8 pages. [18] Johnson, M.A. and Taaffe, M.R. (1989) Matching moments to phase distributions: mixtures of Erlang distributions of common order. Stochastic Models 5, 711-743. [19] Kamalja, K.K. (2017) Reliability computing method for a generalized k-out-of-n system. Journal of Computational and Applied Mathematics, 323, 111¿122. [20] Kendall, D. G. (1951) Some problems in the theory of queues. J. Royal Statist. Soc. B, 13, 151-185. [21] Kendall, D. G. (1953) Stochastic processes occurring in the theory of queues and their analysis by the method of imbedded Markov chains, Ann. Math. Statist., 24, 338-354. [22] Kim, H. and Kim, P. (2017) Reliability¿redundancy allocation problem considering optimal redundancy strategy using parallel genetic algorithm. Reliability Engineering and System Safety, 159, 153¿160. [23] Kulkarni, V.G. (1999) Modeling, analysis, design and control of stochastic systems. Springer-Verlag, New York. [24] Laggounea, R.; Chateauneuf, A. and Aissania, D. (2010) Preventive maintenance scheduling for a multi-component system with non-negligible replacement time. International Journal of Systems Science, vol. 41, no. 7, pp. 747¿761. [25] Levitin, G.; Finkelstein, M. and Dai, Y. (2017a) Redundancy optimization for series-parallel phased mission systems exposed to random shocks. Reliability Engineering and System Safety, 167, 554¿560. [26] Levitin, G.; Jia, H.; Ding, Y.; Song, Y. and Dai, Y. (2017b) Reliability of multi-state systems with free access to repairable standby elements. Reliability Engineering and System Safety, 167, 192¿197. [27] Levitin, G.; Xing, L. and Dai, Y. (2014) Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems. European Journal of Operational Research, 234, 155¿162. [28] Li, W. and Pham, H. (2005) Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks. IEEE Transactions on Reliability, vo. 54, no. 2, pp. 297¿303. [29] Li, Y.; Cui L. and Lin C. (2017) Modeling and analysis for multi-state systems with discrete-time Markov regime-switching. Reliability Engineering and System Safety, 166, 41-49. [30] Lisnianski, A. and Frenkel, I. (2012). Recent advances in system reliability: Signatures, multi-state systems and statistical inference . Springer-Verlag London Limited . [31] Lisnianski, A.; Frenkel, I. and Ding, Y. (2010) Multi-state system reliability analysis and optimization for engineers and industrial managers. Springer-Verlag London. [32] Lisnianski, A.; Frenkel, I. and Khvatskin, L. (2017) On sensitivity analysis of aging multi-state system by using LZ-transform. Reliability Engineering and System Safety, 166, 99¿108. [33] Liu, Z.; Ma, X. Shenc, L. and Zhaob, Y. (2016) Degradation-shock-based Reliability Models for Fault-tolerant Systems. Quality and Reliability Engineering International, 32, 3, 949¿955. [34] Lucantoni, DM (1991) New results on single server queue with a batch Markovian arrival process. Stochastic Models, 7, 1¿46. [35] Mahfoud, H .; El Barkany, A. and El Biyaali, A. (2016) Preventive Maintenance Optimization in Healthcare Domain: Status of Research and Perspective, vol. 2016, Article ID 5314312, 10 pages. [36] Markopoulos, T. and Platis, A.N. (2017) Reliability analysis of a modified IEEE 6BUS RBTS multi-state system. In:Recent advances in multi-state systems reliability, 301¿319. Springer. [37] Minh, D.L. (1978) The discrete-time single-server queue with time-inhomogenous compound Poisson input and general service-time distribution. J. Appl. Prob., 15, 590¿601. [38] Murchland, J. (1975) Fundamental concepts and relations for reliability analysis of multistate systems, In: Barlow, R.E., Fussell, J.B. and Singpurwalla, N. (eds) Reliability and fault tree analysis: theoretical and applied aspects of system reliability. SIAM, Philadelphia, pp. 581¿618. [39] Nakagawa, T. (2005) Maintenance Theory on Reliability. Springer Series in Reliability Engineering series. Springer-Verlag London Limited. [40] Natvig, B. (1985) Multi-state coherent systems. In: Jonson N, Kotz S (eds) Encyclopedia of statistical sciences, 5, 732¿735. Wiley, New York. [41] Neuts, M.F. (1979) A versatile Markovian point process. Journal of Applied Probability, 16, 764-779. [42] Neuts, M.F. (1981) Matrix geometric solutions in stochastic models. An algorithmic approach, Baltimore: John Hopkins University Press. [43] Neuts, M.F. (1992) Models based on the Markovian arrival process. IEICE Trans Commun E75- B, 1255¿1265. [44] Neuts, M.F. (1975) Probability Distributions of Phase Type. In: Emeritus H Florin, editor. Liber Amicorum. Belgium: Department of Mathematics, University of Louvain, 173¿206. [45] Neuts, M.F. and Klimko, E.M. (1973). The single server queue in discrete-time--Numerical analysis I. Naval Res. Logist. Quart, 20, 297-304. [46] Okamura, H.; Dohi, T. and Trivedi, K.S. (2009) Markovian Arrival Process parameter estimation with group data. IEEE/ACM Transactions on networking, 17, 4, 1326¿1339. [47] Osaki, S. and Asakura, A. (1970) A two-unit standby redundant system with repair and preventive maintenance. Journal of Applied Probability, vol. 7, pp. 641-648. [48] Peng, R.; Xiao, H. and Liu, H. (2017) Reliability of multi-state systems with a performance sharing group of limited size. Reliability Engineering and System Safety, 166, 164¿170. [49] Qiu, Q.; Cui, L. and Gao, H. (2017) Availability and maintenance modelling for systems subject to multiple failure modes. Computers & Industrial Engineering, 108, 192¿198. [50] Ramírez-Cobo, P; Lillo, R.E. and Wiper, M.P. (2010) Nonidentifiability of the two-state markovian arrival process. Journal of Applied Probability, 47, 630¿649. [51] Rodríguez, J.; Lillo, R.E. and Ramírez-Cobo, P. (2015) Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process. Reliability Engineering and System Safety, 134, 126¿133. [52] Ruiz-Castro, J.E. (2018) A D-MMAP to model a complex multi-state system with loss of units. In: Recent advances in Multi-state systems Reliability. Anatoly Lisnianski, Ilia Frenkel and Alex Karagrigoriou (Eds), pp. 39¿59. Springer. [53] Ruiz-Castro, J.E. (2013) A preventive maintenance policy for a standby system subject to internal failures and external shocks with loss of units. International Journal of Systems Science, 46, 9, 1600¿1613. [54] Ruiz-Castro, J.E. (2016a) Complex multi-state systems modelled through Marked Markovian Arrival Processes. European Journal of Operational Research, 252, 3,852-865. [55] Ruiz-Castro, J.E. (2016b) Markov counting and reward processes for analyzing the performance of a complex system subject to random inspections. Reliability Engineering and System Safety, vol. 145, pp. 155¿168. [56] Ruiz-Castro, J.E. (2014) Preventive maintenance of a multi-state device subject to internal failure and damage due to external shocks. IEEE Transactions on Reliability, 63, 2, 646-660. [57] Ruiz-Castro, J.E: and Dawabsha. M. (2017) A Markovian arrival process with marked transitions to model a complex system with loss of units. Proceedings European Meeting of Statisticians, EMS 2017. [58] Ruiz-Castro, J.E. and Dawabsha, M. (2017). Modeling a complex multi-state warm standby system with loss of units through a D-MMAP, In proceedings 10th International Conference of the ERCIM Working Group on Computational and Methodological Statistics, CMStatistics 2017. [59] Ruiz-Castro, J.E. and Dawabsha, M. (2017). Modeling a redundant multi-state system with loss of units through a MMAP, In proceedings 10th International Conference on Mathematical Methods in Reliability, MMR 2017. [60] Ruiz-Castro and Dawabsha, M. (2018). Modelización y optimización de un sistema multi-estado de fiabilidad mediante un proceso de llegadas markovianas marcadas. In proceedings XXXVII Congreso Nacional SEIO, SEIO 2018. [61] Ruiz-Castro, J.E. and Dawabsha, M. (2018) Modelling a multi-state k-out-of-n: G system with loss of units. In: Reliability Engineering. Theory and Applications. Ilia Vonta and Mangey Ram(Eds). Taylor and Francis/CRC Press (in press). [62] Ruiz-Castro, J.E.; Dawabsha, M. and Alonso, F.J. (2018) Discrete-time markovian arrival processes to model multi-state complex systems with loss of units and an indeterminate variable number of repairpersons. Reliability Engineering and System Safety, 174, 114-127. [63] Ruiz-Castro, J.E. and Fernández-Villodre, G. (2012) A complex discrete warm standby system with loss of units. European Journal of Operational Research, 218, 456-469. [64] Ruiz-Castro, J. E and Li, Q.-L. (2011) Algorithm for a general discrete k-out-of-n: G system subject to several types of failure with an indefinite number of repairpersons. European Journal of Operational Research, 211, 97¿11. [65] Shatnawi, O. (2016) An integrated framework for developing discrete-Time modelling in software reliability engineering, Quality and Reliability Engineering International, 32, 8, 2925¿2943. [66] Warrington, L. and Jones, J.A. (2003) Representing Complex Systems within Discrete Event Simulation for Reliability Assessment. Proceedings Annual Reliability and Maintainability Symposium, 487-492. [67] Wells, C.E. (2014) Reliability analysis of a single warm-standby system subject to repairable and nonrepairable failures. European Journal of Operational Research, 235, 1, 180¿186. [68] Xie, Y.; Zhang, J.; Aldemir, T. and Denning, R. (2018) Multi-state Markov modeling of pitting corrosion in stainless steel exposed to chloride-containing environment. Reliability Engineering and System Safety, 172, 239¿248. [69] Yeh, C.-T. and Fiondella, L. (2017) Optimal redundancy allocation to maximize multi-state computer network reliability subject to correlated failures. Reliability Engineering and System Safety, 166, 138¿150. [70] Yi, H. and Cui, L. (2017) Distribution and availability for aggregated second-order semi- Markov ternary system with working time omission. Reliability Engineering and System Safety, 166, 50¿60. [71] Yongjin, Z.; Youchao, S.; Longbiao, L. and Ming Z. (2018) Copula-based reliability analysis for a parallel system with a cold standby. Communications in Statistics: Theory and Methods, 47, 3, 562¿582. [72] Zhang, Y.L. and Wang, G.J. (2011) An extended replacement policy for a deteriorating system with multi-failure modes. Applied Mathematics and Computation, 218, 1820¿1830. [73] Zhong, C.Q. and Jin, H. (2014) A novel optimal preventive maintenance policy for a cold standby system based on semi-Markov theory. European Journal of Operational Research, 232, 405¿411.

Imprimir

Modificar Consulta Nueva Consulta

Versión 4.4